Fermionic spinon theory of square lattice spin liquids near the Néel state

Abstract

Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a ${\mathbb{CP}}^1$ theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge 2 Higgs fields, deconfined phases with ${\mathbb{Z}}_2$ topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in $\pi$-flux in each square lattice plaquette. Fluctuations about this $\pi$-flux state are described by 2+1 dimensional quantum chromodynamics (QCD${}_3$) with a SU(2) gauge group and $N_f=2$ flavors of massless Dirac fermions. It has recently been argued by Wang et al. (arXiv:1703.02426) that this QCD${}_3$ theory describes the Néel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD${}_3$, and obtain fermionic dual descriptions of the phases with ${\mathbb{Z}}_2$ topological order obtained earlier using the bosonic ${\mathbb{CP}}^1$ theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state. The global phase diagram of these phases contains multi-critical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.

Version 2: 32 pages, 3 figures, 12 tables; fixed typos, merged figures

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